Question

The marks obtained by $50$ students of class $10$ out of $80$ marks are given in the following frequency distribution. Find the median.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$2$	$5$	$8$	$16$	$9$	$5$	$3$	$2$

Answer 1

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$2$	$5$	$8$	$16$	$9$	$5$	$3$	$2$
Cumulative Frequency	$2$	$7$	$15$	$31$	$40$	$45$	$48$	$50$

Total number of students$=n=50$

$\frac{n}{2}=\frac{50}{2}=25$,

As $25<31$,

So $30-40$ is the median class.

$l$ is the lower limit of median class, so $l=30$

$h$ is the size of class interval, so $h=40-30=10$

$f$ is the frequency of median class, so $f=16$

$F$ is the cumulative frequency of class preceding the median class, so $F=15$

$Median=l+\left(\frac{\frac{n}{2}-F}{f}\right)\times h$

$Median=30+\left(\frac{\frac{50}{2}-15}{16}\right)\times 10$

$Median=30+\left(\frac{10}{16}\right)\times 10$

$Median=30+\left(\frac{100}{16}\right)$

$Median=36.25$

Hence, the median is$=36.25$